We present D$^2$CSG, a neural model composed of two dual and complementary network branches, with dropouts, for unsupervised learning of compact constructive solid geometry (CSG) representations of 3D CAD shapes. Our network is trained to reconstruct a 3D shape by a fixed-order assembly of quadric primitives, with both branches producing a union of primitive intersections or inverses. A key difference between D$^2$CSG and all prior neural CSG models is its dedicated residual branch to assemble the potentially complex shape complement, which is subtracted from an overall shape modeled by the cover branch. With the shape complements, our network is provably general, while the weight dropout further improves compactness of the CSG tree by removing redundant primitives. We demonstrate both quantitatively and qualitatively that D$^2$CSG produces compact CSG reconstructions with superior quality and more natural primitives than all existing alternatives, especially over complex and high-genus CAD shapes.

翻译：我们提出D$^2$CSG——一种由两个对偶互补网络分支（含丢弃策略）组成的神经模型，用于三维CAD形状的紧凑型结构实体几何（CSG）表示的无监督学习。该网络通过固定顺序的二次基元装配来重建三维形状，两个分支分别生成基元交集或逆运算的并集。D$^2$CSG与所有先前神经CSG模型的关键区别在于其专用残差分支，用于组装可能复杂的形状补集，该补集从覆盖分支建模的整体形状中减去。通过引入形状补集，该网络具有可证明的通用性，而权重丢弃策略通过移除冗余基元进一步提升了CSG树的紧凑性。定量与定性实验表明，相较于现有替代方案（尤其在处理复杂高亏格CAD形状时），D$^2$CSG能生成具有更优质量和更自然基元的紧凑CSG重建结果。